Only 3 and 7

Find the smallest positive integer \(N\) such that:

  • Each digit of \(N\) is 3 or 7.
  • \(N\) is divisible by 3 and 7.
  • The sum of digits in \(N\) is divisible by 3 and 7.
  • \(N\) ends in a 3.
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